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Grade 11 · 35 knowledge points · 169 sub-skills · Browse every skill by grade and topic.

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SkillsMap

A. Number

  1. 1Number and Number Systems
    3 sub-skills
    1. 1aAdditive or positional? Comparing numeration systems
    2. 1bWhy zero was such a big deal
    3. 1cHow Hindu-Arabic numerals took over Europe
  2. 2Real Number System with Rational Exponents
    5 sub-skills
    1. 2aSorting out the real numbers
    2. 2bnth roots and radical notation
    3. 2cRational exponents ↔ radicals
    4. 2dEvaluating powers with rational exponents
    5. 2eExponent laws with rational exponents

B. Patterns & Algebra

  1. 1Forms of Mathematical Reasoning
    6 sub-skills
    1. 1aMaking a conjecture from a pattern
    2. 1bDisproving with a counterexample
    3. 1cTelling inductive from deductive reasoning
    4. 1dBuilding a deductive argument
    5. 1eFinding the flaw in a fake proof
    6. 1fReasoning out a winning strategy
  2. 2Linear and Quadratic Inequalities
    5 sub-skills
    1. 2aLinear inequalities in one variable
    2. 2bGraphing linear inequalities in two variables
    3. 2cSystems of linear inequalities
    4. 2dQuadratic inequalities in one variable
    5. 2eQuadratic inequalities in two variables
  3. 3Patterns and Algebra
    3 sub-skills
    1. 3aAlgebra written in sentences
    2. 3bWhat symbols made possible
    3. 3cDifferent cultures, different algebra
  4. 4Polynomial Factoring
    6 sub-skills
    1. 4aCommon factors and factoring by grouping
    2. 4bFactoring ax² + bx + c when a ≠ 1
    3. 4cDifference of squares
    4. 4dRecognizing perfect square trinomials
    5. 4eFactoring when the variable is a bracket
    6. 4fChoosing a method and finishing the job
  5. 5Quadratic Functions and Equations
    6 sub-skills
    1. 5aReading a parabola: vertex, intercepts, domain and range
    2. 5bVertex form y = a(x - p)² + q
    3. 5cCompleting the square: standard form to vertex form
    4. 5dSolving quadratics by factoring
    5. 5eThe quadratic formula and the discriminant
    6. 5fModelling with quadratics: maximum and minimum
  6. 6Radical Operations and Equations
    6 sub-skills
    1. 6aSimplifying radicals (mixed and entire)
    2. 6bAdding and subtracting radicals
    3. 6cMultiplying radicals
    4. 6dDividing and rationalizing denominators
    5. 6eSolving radical equations
    6. 6fRestrictions and extraneous roots
  7. 7Rate of Change
    5 sub-skills
    1. 7aUnit rates on the job
    2. 7bRate of change from a table
    3. 7cReading rate of change off a graph
    4. 7dSlope as roof pitch and road grade
    5. 7eUsing a rate to predict and to choose
  8. 8Rational Expressions and Equations
    6 sub-skills
    1. 8aNon-permissible values
    2. 8bSimplifying rational expressions
    3. 8cMultiplying and dividing rational expressions
    4. 8dAdding and subtracting rational expressions
    5. 8eSolving rational equations
    6. 8fSetting up rate and shared-work problems

C. Geometry & Measurement

  1. 13D Objects: Angles, Views, and Scale Diagrams
    5 sub-skills
    1. 1aTop, front and side views
    2. 1bNets: flattening a solid out
    3. 1cReading a scale diagram or blueprint
    4. 1dDrawing your own scale diagram
    5. 1eAngles on the site: keeping things square
  2. 2Angle Relationships
    5 sub-skills
    1. 2aAngle pairs formed by a transversal
    2. 2bGiving the reason, not just the number
    3. 2cInterior and exterior angle sums
    4. 2dChains of reasoning in a diagram
    5. 2eProving an angle conjecture
  3. 3Geometry
    3 sub-skills
    1. 3aGeometry started as land measurement
    2. 3bEuclid and the axiomatic method
    3. 3cThe parallel postulate and non-Euclidean geometry
  4. 4Scale Models
    5 sub-skills
    1. 4aScale factor and lengths
    2. 4bReading and making scale drawings
    3. 4cWhy area scales by k²
    4. 4dWhy volume scales by k³
    5. 4eDeciding whether two objects are similar
  5. 5Trigonometry: Non-right Triangles and Angles in Standard Position
    6 sub-skills
    1. 5aAngles in standard position and reference angles
    2. 5bTrig ratios of any angle
    3. 5cFinding all angles from 0° to 360°
    4. 5dThe sine law
    5. 5eThe ambiguous case (SSA)
    6. 5fThe cosine law

D. Data & Probability

  1. 1Applications of Statistics
    5 sub-skills
    1. 1aStandard deviation: how spread out is it?
    2. 1bThe normal distribution and the 68-95-99.7 rule
    3. 1cz-scores: comparing across different scales
    4. 1dConfidence intervals and margin of error
    5. 1eJudging whether a claim is supported
  2. 2Graphical Analysis
    5 sub-skills
    1. 2aThe region of a linear inequality
    2. 2bFeasible region of a system
    3. 2cTurning a situation into constraints
    4. 2dFinding and defending the optimal solution
    5. 2eReading a quadratic graph
  3. 3How Probability and Statistics Are Used in Different Contexts
    5 sub-skills
    1. 3aProbability on the shop floor
    2. 3bOdds versus probability
    3. 3cMaking sense of risk statements
    4. 3dMean, median or mode — which one is honest here?
    5. 3eRange, outliers and what they do to your numbers
  4. 4Interpreting Graphs in Society
    5 sub-skills
    1. 4aReading the graphs you actually meet
    2. 4bInfographics and double-axis graphs
    3. 4cWhen the axis is doing the lying
    4. 4dWhen the data or the labels are doing the lying
    5. 4eChoosing the right graph and defending it
  5. 5Probability and Statistics
    3 sub-skills
    1. 5aProbability was born at the gambling table
    2. 5bCounting people: censuses, death tables, insurance
    3. 5cThe 'average man' and where it went wrong

E. Computer Science

  1. 1Basic Programming Concepts
    5 sub-skills
    1. 1aVariables and assignment
    2. 1bExpressions and operators
    3. 1cSequence: tracing line by line
    4. 1dInput, output and formatting
    5. 1eReading errors: syntax, runtime, logic
  2. 2Cryptography
    3 sub-skills
    1. 2aSubstitution ciphers and the Caesar shift
    2. 2bFrequency analysis and the code-breaking arms race
    3. 2cThe public-key idea
  3. 3Development of Algorithms
    5 sub-skills
    1. 3aFrom problem to precise steps
    2. 3bAccumulators: total, count, max
    3. 3cTrace tables for loops
    4. 3dDesigning test cases
    5. 3eNarrowing down a bug
  4. 4Problem Decomposition Through Modularity
    5 sub-skills
    1. 4aOne function, one job
    2. 4bDefining and calling a function
    3. 4cBreaking a problem into functions
    4. 4dSpotting duplication and factoring it out
    5. 4ePutting the pieces back together
  5. 5Techniques for Operations On and Searching of Arrays and Lists
    5 sub-skills
    1. 5aLists and indexing from zero
    2. 5bTraversing a list
    3. 5cInserting and deleting shifts everything
    4. 5dLinear search
    5. 5eBinary search on sorted data
  6. 6Tools and Technology
    3 sub-skills
    1. 6aAbacus, counting rods and quipu
    2. 6bLogarithms: turning multiplication into addition
    3. 6cFrom gears to circuits
  7. 7Use of Control Flow
    6 sub-skills
    1. 7aif / elif / else
    2. 7bNested conditions
    3. 7cwhile loops: making them stop
    4. 7dfor loops and ranges
    5. 7eOff-by-one errors
    6. 7fNested loops
  8. 8Uses of Computing for Financial Analysis
    5 sub-skills
    1. 8aMoney, floats and rounding
    2. 8bSimple and compound interest in code
    3. 8cBuilding a loan payment schedule
    4. 8dSummarising transaction data
    5. 8eComparing financial scenarios
  9. 9Variable Scope
    4 sub-skills
    1. 9aLocal vs global variables
    2. 9bParameters vs arguments
    3. 9cReturning a value vs printing it
    4. 9dShadowing and why globals bite
  10. 10Ways to Construct and Evaluate Logical Statements
    5 sub-skills
    1. 10aComparison operators
    2. 10band, or, not — truth tables
    3. 10cBuilding compound conditions
    4. 10dNegating a condition correctly
    5. 10eShort-circuit evaluation and test order
  11. 11Ways to Model Mathematical Problems
    5 sub-skills
    1. 11aTurning a formula into an expression
    2. 11bApproximating by iterating
    3. 11cSimulating with random numbers
    4. 11dTabulating values to find a threshold
    5. 11eChecking that the answer is believable
  12. 12Ways to Represent Basic Data Types
    5 sub-skills
    1. 12aThe basic data types
    2. 12bIntegers vs floating point
    3. 12cStrings are sequences of characters
    4. 12dConverting between types
    5. 12eHow data is stored in binary

F. Financial Literacy

  1. 1Financial Literacy
    5 sub-skills
    1. 1aHow compound interest grows money
    2. 1bComparing two investment offers
    3. 1cThe real cost of borrowing
    4. 1dRent, buy or lease — and defend it
    5. 1eWhat is this ad not telling you?
  2. 2Financial Literacy: Compound Interest, Investments, Loans
    5 sub-skills
    1. 2aSimple interest vs compound interest
    2. 2bThe compound interest formula
    3. 2cCompounding periods and effective rates
    4. 2dComparing investment options
    5. 2eLoans and the cost of credit
  3. 3Financial Literacy: Personal Investments, Loans, and Budgeting
    5 sub-skills
    1. 3aInterest on a real savings account
    2. 3bSavings account, GIC, TFSA: which one?
    3. 3cCar loans and monthly payments
    4. 3dCredit cards and the minimum payment trap
    5. 3eBuilding a monthly budget that balances